Yes, if you had taxable income during the months you lived in West Virginia. You would file as a part year resident for both states if you had taxable income in each state.
Report the income you received while you resided in WV using a part year residency status. Since you lived there with your daughter for four months, any income you received while living there is required to be reported on the WV return.
You can determine the income for each state based on what your actually received will living there. If the Forms 1099R represent that amount, then use it as the amount that is taxable. Otherwise use the amount you actually received by checking your bank or other record (gross amount must be used for tax purposes).
Social Security benefits and other types of retirement income are taxed in West Virginia but seniors can claim a deduction to offset those taxes so watch the questions that come up when completing that return.
Georgia also has a retirement exclusion. Taxpayers who are 62 or older, or permanently and totally disabled regardless of age, may be eligible for a retirement income adjustment on their Georgia tax return. Retirement income includes: Income from pensions and annuities. Watch the questions while completing this return as well.